He's saying he'll be having sex with you. No more complicated than that

Hilary has given a really good answer.

As Hillary says in her comment, "do someone" in certain contexts usually refers to sex. Given the context, also taking into account the body language and tone, "doing" could be taken to be just a creative play on words, for example companionship rather than only sex. I can say I am doing more art these days. "doing" can be used as you intended, generally. His response could have been intended in the same way.

moved

To "do" someone is another way of saying to have sex with someone. So he is saying that he imagines that he will still be sleeping with you in ten years. It's a cheeky way of saying he's hoping you two are still together long-term... and still having fun. ;)